Abstract: J42.00001 : Cyclic competition of four or more species: Results from mean field theory and stochastic simulations*

Author:

R.K.P. Zia(Physics Department, Virginia Tech, Blacksburg, VA 24061)

Population dynamics is a venerable subject, dating back two centuries to
Malthus, Verhulst, Lotka, Volterra, and many others. Nonetheless, new and
interesting phenomena are continually being discovered. For example, the
recent discovery of ``Survival of the Weakest'' in cyclic competition
between 3 species with no spatial structure (Berr, Reichenbach,
Schottenloher, and Frey, Phys. Rev. Lett. 102, 048102 (2009)) attracted
considerable attention, e.g.,
http://www.sciencedaily.com/releases/2009/02/090213115127.htm. Considering a
similar system with 4 or more species, we find a more intuitively
understandable principle which appears to underpin all systems with
cyclically competing species. We will present several interesting aspects of
the 4 species system -- from non-linear dynamical phenomena in a
deterministic mean-field approach to remarkable extinction probabilities in
the stochastic evolution of a finite system. Some insights into the
deterministic dynamics, gained from generalizing this system to one with any
number of species with arbitrary pairwise interactions, will also be
discussed.

*Supported in part by NSF-DMR-0904999 and 1005417.

To cite this abstract, use the following reference: http://meetings.aps.org/link/BAPS.2012.MAR.J42.1